What is sin(arctan(L/y)) ?

The solution to sin(arctan(L/y)) is (Lsqrt(y^2+L^2))/(y^2+L^2)

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simplify sin(arctan(L/y))

simplify

sin (arctan (\frac{L}{y}))

\frac{L y ^{2} + L ^{2}}{y ^{2} + L ^{2}}

Solution steps

sin (arctan (\frac{L}{y}))

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{L}{y} ) 1 + ( \frac{L}{y} ) ^{2}}{1 + ( \frac{L}{y} ) ^{2}}

Simplify

= \frac{L y ^{2} + L ^{2}}{y ^{2} + L ^{2}}

3 cos (x + \frac{2 π}{3})

csc (arccos (1 + 3 x))

- 4 π sin (10 π t - \frac{π}{3})

15 - 13 cos (10 x + π)

cos (x - \frac{5 π}{4})

What is sin(arctan(L/y)) ?
The solution to sin(arctan(L/y)) is (Lsqrt(y^2+L^2))/(y^2+L^2)